Mathematics > Algebraic Geometry

Title:Every rational Hodge isometry between two K3 surfaces is algebraic

Abstract: We prove that given any rational Hodge isometry
$ψ:H^2(S_1,\mathbb{Q})\rightarrow H^2(S_2,\mathbb{Q})$ between any two
Kähler $K3$ surfaces $S_1$ and $S_2$ the cohomology class of $ψ$ in
$H^{2,2}(S_1\times S_2)$ is a polynomial in Chern classes of coherent analytic
sheaves over $S_1 \times S_2$. Consequently, the cohomology class of $ψ$ is
algebraic whenever $S_1$ and $S_2$ are algebraic.